Ask question

Ask question

All categories

2 years ago

15

The value of y varies directly with x. When y = 75, x = ½ . What is the value of y when x is 2 ¼ ? A. 168.75 C. 66.67 B. 16.67 D

. 337.5

1 answer:

lora16 [44]2 years ago

8 0

Answer:

Step-by-step explanation:

The value of y varies directly with x. When y = 75, x = ½ . What is the value of y when x is 2 ¼ ? A. 168.75 C. 66.67 B. 16.67 D. 337.5

y ∝x

y = kx

k = y/x

You might be interested in

Two runners are saving money to attend a marathon. The first runner has $110 in savings, received a $45 gift from a friend, and

Nikitich [7]

Whats the question? :)

3 0

3 years ago

On Tuesday a local hamburger shop sold a combined total of 345 hamburgers and cheeseburgers the number of cheeseburgers sold was

spayn [35]

The equation is:
$h + c = 345 \\ \\ c = 2h$
Replace c with 2h:
$h + 2h = 345 \\ \\ 3h = 345$
Divide both sides by 3:
$h = 115$

7 0

3 years ago

25) Norachai had some candy to give to his

Sphinxa [80]

Answer:

30

Step-by-step explanation:

He took 5 pieces.

His children took 5 * 5 pieces = 25

The total is 5 + 25 = 30.

8 0

3 years ago

Point Y is in the interior of ∠XWZ. Given that (ray) WX and (ray) WZ are opposite rays and m∠XWY = 4(m∠YWZ), what is m∠YWZ?

yuradex [85]

Answer:

m∠YWZ = 36°

Step-by-step explanation:

* Lets explain how to solve the problem

- Point Y is in the interior of ∠XWZ

- Rays WX and WZ sre opposite rays

- That means rays WX and WZ formed a straight angle

- m∠XWY = 4(m∠YWZ)

- We need to find the m∠YWZ

* Lets solve the problem

∵ Rays WX and WZ are opposite rays

∴ ∠XWZ is a straight angle

∵ The measure of the straight angle is 180°

∴ m∠XWZ = 180°

- Point Y is in the interior of ∠XWZ

∴ m∠XWZ = m∠XWY + m∠YWZ

∵ m∠XWY = 180°

∴ m∠XWY + m∠YWZ = 180° ⇒ (1)

∵ m∠XWY = 4(m∠YWZ) ⇒ (2)

- Substitute equation (2) in equation (1)

- That means replace m∠XWY by 4(m∠YWZ)

∴ 4(m∠YWZ) + m∠YWZ = 180

∴ 5(m∠YWZ) = 180

- Divide both sides by 5

∴ m∠YWZ = 36°

6 0

4 years ago

Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at the point (3, 4) in sl

Wittaler [7]

Answer:

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

Step-by-step explanation:

The equation of a circle of radius $5$ centered at $(0,0)$ is:

$x^{2} + y^{2} = 5^{2}$ .

$x^{2} + y^{2} = 25$ .

Differentiate implicitly with respect to $x$ to find the slope of tangents to this circle.

$\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]$

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(y^{2}) = 0$ .

Apply the power rule and the chain rule. Treat $y$ as a function of $x$ , $f(x)$ .

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(f(x))^{2} = 0$ .

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}(2f(x)\cdot f^{\prime}(x)) = 0$ .

That is:

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}\left(2y \cdot \frac{dy}{dx}\right) = 0$ .

Solve this equation for $\displaystyle \frac{dy}{dx}$ :

$\displaystyle \frac{dy}{dx} = -\frac{x}{y}$ .

The slope of the tangent to this circle at point $(3, 4)$ will thus equal

$\displaystyle \frac{dy}{dx} = -\frac{3}{4}$ .

Apply the slope-point of a line in a cartesian plane:

$y - y_0 = m(x - x_0)$ , where

$m$ is the gradient of this line, and
$(x_0, y_0)$ are the coordinates of a point on that line.

For the tangent line in this question:

$\displaystyle m = -\frac{3}{4}$ ,
$(x_0, y_0) = (3, 4)$ .

The equation of this tangent line will thus be:

$\displaystyle y - 4 = -\frac{3}{4} (x - 3)$ .

That simplifies to

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

3 0

3 years ago